11.34 (1990)

Open

Describe the complex representations of quasisimple finite groups which remain irreducible after reduction modulo any prime number $q$. An important example: representations of degree $(p^k - 1)/2$ of the symplectic group $Sp(2k, p)$ where $k \in \mathbb{N}$ and $p$ is an odd prime.

Progress

See partial results in (P. H. Tiep, Preprint, 2023, https://arxiv.org/abs/2411.16379).

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